Geodesic
To the theory of synchronization of interacting pendulums oscillating in the parallel planes
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 15-37

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of interacting metal pendulums oscillating in parallel planes, the distance $b$ between the suspension points of which is fixed and equally, has been solved. The principle possibility of their synchronization is provided by taking into account two physical factors: 1. Effect of electromagnetic interaction between them and 2. Accounting for EM radiation of each pendulum, leading to non-linear attenuation. The system of nonlinear dynamic motion equations obtained by a strict mathematical path is analyzed, and their numerical solution is given. The article offers a new method for constructing the pairs of function which are holomorphic on the whole complex plane and satisfy functional equations such as the addition theorem for theta functions. 
@article{DVMG_2020_20_1_a2,
     author = {S. O. Gladkov and S. B. Bogdanova},
     title = {To the theory of synchronization of interacting pendulums oscillating in the parallel planes},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {15--37},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a2/}
}
TY  - JOUR
AU  - S. O. Gladkov
AU  - S. B. Bogdanova
TI  - To the theory of synchronization of interacting pendulums oscillating in the parallel planes
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2020
SP  - 15
EP  - 37
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a2/
LA  - ru
ID  - DVMG_2020_20_1_a2
ER  - 
%0 Journal Article
%A S. O. Gladkov
%A S. B. Bogdanova
%T To the theory of synchronization of interacting pendulums oscillating in the parallel planes
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2020
%P 15-37
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a2/
%G ru
%F DVMG_2020_20_1_a2
S. O. Gladkov; S. B. Bogdanova. To the theory of synchronization of interacting pendulums oscillating in the parallel planes. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 15-37. http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a2/